Introduction to Determinism and Quantum Mechanics

The following is an email I sent to my friend Bryant Johnson a conversation we had about determinism. There are no pictures, so I might have to adjust the writting a bit later, so it's more stand alone. A good deal of what I know about the philosophy of quantum mechanics is due to the first section of a spendid book by Hans Reichenbach called, "Philosophic Foundations of Quantum Mechanics".

Dear Bryant,

I’m writing this in response to the conversation we had outside of Hyde dorm yesterday. I’m writing about how scientific discoveries within the last hundred years have done much to undermine notions of determinism which were largely accepted in the 19th and early 20th centuries. Before I embark on an explanation, of course realize that I am more of a philosopher than a physicist, and thus do not pretend to have too firm a grasp on quantum mechanics, especially as formulated mathematically. I will endeavor to limit myself to explaining some of the more basic elements of quantum mechanics in order to avoid wandering into areas where my knowledge is far less trustworthy. As I always say, to know what you’re talking about, talk about what you know.

Before addressing whether or not our world is a deterministic one, it’s an essential first step to talk about what determinism means, as the word is used in different senses in different settings. Specifically, I would like to make a distinction between epistemological determinism and determinism proper. Bountiful scientific evidence has been supplied against the former, while there is good reason to believe that no evidence can be supplied before or against the latter. If our world is epistemologically deterministic, it means that if we know everything there is to know about the universe at an initial time, we can calculate everything that there is to know about the universe at a later time. Determinism in the epistemological sense, then, has to do with our abilities to know the future.

Determinism proper, by contrast, means that given a state of the universe an initial time, there is only one possible state of affairs at a later time. This is best illustrated by an example. Suppose that we used the Cosmic Remote to rewind the universe to the earliest stages of the big bang. We then hit the play button. If the universe turns out exactly the same as it is today, from the organization of galaxies to atoms, then our world is deterministic. If it turns out to be different in the slightest, then our world is not deterministic.

It is Heisenberg’s uncertainty principle that provides strong evidence that we do not live in an epistemologically deterministic world—there are inherent physical limits as to how accurately we can predict the future. It used to be believed that if one could assess the momentum and position of every particle in the universe accurately enough then it would be theoretically possible, though consummately impractical, to predict the momentum and position of particles in the universe at future states. Since Heisenberg’s uncertainty principle places a fundamental limit on the accuracy with which we can determine the momentum and position of a particle. The more accurately we know the momentum of a particle, the less accurate it is possible to measure the position of a particle. Similarly, the more accurately we know the position of a particle, the less accurately it is possible to measure the position of a particle. Since you cannot measure momentum and position of present particles to an arbitrary degree of accuracy, you cannot calculate the momentum and position of future particles to an arbitrary degree of accuracy.

This is not, however, the whole story. Even after supplying strong evidence against epistemological determinism, it is entirely possible that the universe could be deterministic, comprised of an unbroken chain of cause and effect. The problem is that if this is the case, due to Heisenberg’s uncertainty principle, we can never know it. There may be some unseen mechanism underlying the probabilistic science of quantum mechanics, but it is by its nature unobservable. I will explain why this is so by taking you through the astounding and paradoxical double slit experiment. This will be a bit of an aside, but you may find it interesting, and it will explain why science as it currently stands suggests that we cannot know.

There came a point in the 1800’s when physicists began to believe that they were finally beginning to fill in the holes in their picture of the universe. All that was left was to determine the nature of that most mysterious of phenomena—light. Scientists conducted a series of experiments to find out whether light was a wave or a particle. The most important of these was the double slit experiment by Thomas Young in 1803. It works as follows. A concentrated beam of light is aimed at a thin vertical slit in an opaque sheet. On the other side of the sheet from the source of light is a photosensitive screen on which you can see the pattern the light makes as it “scatters” through the slit. This pattern is known as the “interference pattern.”
When beaming the light at the slit, the light spread out slightly. What showed up on the photo screen afterwards was not simply a shadow of light behind the slit—it was more spread out. As interesting as this is, it’s trivial compared to the result that happens in the following variation: what happens if you aim the beam of light at two narrow slits very close together? What happens is counter intuitive. Instead of seeing two narrow slits of light on the photo sensitive screen, you see alternating bands of light and dark!

You can see what the bands look like from the picture above. The circles take some explanation, as they are the reason light is said to have a “wave nature” as well as a “particle nature”. The circles are simply how one would determine ahead of time the density of light at a various regions of the photosensitive sheet. You simply visualize light as waves radiating outward from the slits as if from two rocks dropped next to each other in a pool of water. Depending on the way these “waves” cross one another, they are said to be interfering (interacting) in a “constructive” manner, a “destructive” manner, or somewhere in between. Interference that is more constructive in nature corresponds to a lighter patch on the photo screen, and interference that is more destructive in nature corresponds to a dimmer patch on the photo screen. I realize that this is far from clear, but hopefully another picture I bummed off of Google will help demonstrate the point:

The point is that light appears to interact in a wave like way in the same way that matter seems to interact in a particle light way. Thus, for several decades, scientists believed that light had an exclusively wave like nature and matter had an exclusively particle like nature. This assumption was destroyed by new discoveries that were made in the 20th century. First of all, Planck discovered that light was actually emitted in discrete particles or “quanta” called photons. Secondly, it is not known that the experiment described above works for electrons as well as photons, suggesting that both photons and electrons have both a particle nature and a wave nature.
As mentioned above, the interference patterns on the screen seem to be due to particles passing through the slits interacting with each other in some way. This raises the question of what would happen if one were to use a device that emitted only one particle at a time (in the case electrons), supposedly depriving the particles of a chance to interact with other particles. Because of this, one would expect electrons to simply build up behind the two slits like an inverse shadow. Thus began an experiment with historically bizarre results. An electron beam was aimed at two slits, and electrons were fired one at a time. The following picture shows the buildup of electrons over time on the photo screen.

The exact same thing happens as did when electrons were emitted simultaneously. Even though the single electron has nothing to interact with, there is still an interference pattern. It appears as if the electron somehow interacts with itself by going through both slits at once! Astonishing. Excited scientific folk immediately set to work to detect if this was the case. If the electron really passed through both slits at once, then it should be possible to detect it doing just that. In order to detect whether the particle passed through one slit, or the other, or both, the experimenters set up detectors at both slits that would go off if an electron passed through that slit.

Something happened that the physicists weren’t counting on. The mere presence of the detectors changed the system so that the interference patterns disappeared, and instead there were the inverse shadows of electrons building up directly behind the two slits. Only one detector went off at a time, depending on which slit the electron passed through. Since the circumstances of the experiment were unexpectedly and radically changed, the original question of which slit the electron passed through remained unanswered. People debate to this day about whether or not there is even a fact of the matter of where the electron is before it hits the photo screen. The question is really one for philosophers now—scientists cannot detect where the electron is beforehand without radically changing the results of the experiment.

This concludes the admittedly lengthy portion of this essay about the experimental results, and I am now in a better position to use these results in order to explain why there is currently no evidence for determinism. The first thing that you will notice is that while one can visualize particles as waves interfering with each other in order to determine the interference pattern, there is no method to determine where an individual particle will hit the screen. Instead, all that can be given is the probability that the particle will hit a certain point on the photo screen.

The first thing that comes to mind upon hearing this is that this probabilistic nature of quantum mechanical predictions must reflect limits on what we can know, rather than an element of nature being fundamentally probabilistic. The problem with this view is that there is simply no evidence to suggest that there is some underlying mechanism that determines ahead of time where the particle hits the screen. In fact, a more recent (1970’s) experiment (that I do not understand nearly as well as the slit experiments suggests that) resulted in a ground-breaking discovery known as Bell’s theorem, which states “No physical theory of hidden variables can ever reproduce all of the predictions of Quantum mechanics.”

Basically, this means that there are no subatomic causal mechanisms that are determining ahead of time where the electron will hit the screen. Assuming the truth of Bell’s theorem, the only way to formulate a physically consistent deterministic theory is to allow nonlocal variables and causality at a distance. Some experiments do result in objects that are separated by great distances but are nevertheless “synchronized” in a way, a phenomena known as entanglement. It the crazy quantum world, non-local causality is a possibility. But as of yet, there is simply no evidence for it at all.

So, while it is still logically possible that our world is deterministic, that the state of the universe at one moment exact ally determines future states, there is no more solid evidence for it than the hypothesis that there are pink sub-atomic rabbits pushing the electrons to their final destination (I love using that example). There are several interpretations of quantum mechanics, some of which are deterministic, such as the Bohme interpretation and Everett’s many worlds interpretation, the first of which involves non-local causality, and the second of which involves an infinite (and growing) number of causally isolated universes constantly branching off from one another. As of yet, no methods have been devised for determining which interpretation is correct, although the Copenhagen interpretation is currently the most common (this is the one that says that there is not fact of the matter of a particles exact position or momentum before it is measured). There is good reason to believe that even a unified theory of physics would be ambiguous with respect to determinism.

Another objection that could be raised to my arguments is the possibility that macroscopic events are practically certain, since quantum effects happen at scales too small to translate into a probabilistic reality. The problem with this objection is that while the macroscopic world isn’t usually subject to quantum uncertainty, it certainly can be under certain circumstances. For example, say that I set up a single slit experiment, and drew a line direct ally down the center of the photo screen. I plan to fire a single particle, and tell myself that if the particle hits to the left of the line then I’ll eat dinner at Moulten and that if the particle hits to the right of the line then I’ll eat dinner at Thorne. If quantum mechanical phenomena really are inherently probabilistic, then I have just made a perfectly random macroscopic decision.

Lastly, it should be mentioned that even if does turn out to be true (although we now have no way of knowing) that our world in inherently probabilistic, it is still possible to accept determinism in a sense, only with a modified definition. Even if events do not strictly determine each other, it appears that at least probabilities directly determine each other. Given the probability distribution of a particle’s position at an initial time, I can compute exactly the probability distribution of the particle’s position at a later time